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991.
Evgeniy Pustylnik Alexander J. Zaslavski 《Numerical Functional Analysis & Optimization》2013,34(5-6):632-645
We study the influence of errors on the convergence of infinite products of nonexpansive mappings in metric spaces. 相似文献
992.
In this paper, we construct an oblique reflecting switched diffusion process and give the Skorohod representation for this process by using the Dirichlet space theory. We show the tightness property for a sequence of these processes. To do this, we extend the Lyons–Zheng decomposition theorem to the oblique reflecting switched diffusion process 相似文献
993.
Anant P. Godbole 《Discrete Mathematics》2009,309(11):3609-3624
Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph, γ(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed. We determine Bose-Einstein and Maxwell-Boltzmann cover pebbling thresholds for the complete graph. Also, we show that the cover pebbling decision problem is NP-complete. 相似文献
994.
The pebbling number of a graph G, f(G), is the least n such that, no matter how n pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of pebbling moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. Let p1,p2,…,pn be positive integers and G be such a graph, V(G)=n. The thorn graph of the graph G, with parameters p1,p2,…,pn, is obtained by attaching pi new vertices of degree 1 to the vertex ui of the graph G, i=1,2,…,n. Graham conjectured that for any connected graphs G and H, f(G×H)≤f(G)f(H). We show that Graham’s conjecture holds true for a thorn graph of the complete graph with every by a graph with the two-pebbling property. As a corollary, Graham’s conjecture holds when G and H are the thorn graphs of the complete graphs with every . 相似文献
995.
A graph G is induced matching extendable, shortly IM-extendable, if every induced matching of G is included in a perfect matching of G. For a nonnegative integer k, a graph G is called a k-edge-deletable IM-extendable graph, if, for every F⊆E(G) with |F|=k, G−F is IM-extendable. In this paper, we characterize the k-edge-deletable IM-extendable graphs with minimum number of edges. We show that, for a positive integer k, if G is ak-edge-deletable IM-extendable graph on 2n vertices, then |E(G)|≥(k+2)n; furthermore, the equality holds if and only if either G≅Kk+2,k+2, or k=4r−2 for some integer r≥3 and G≅C5[N2r], where N2r is the empty graph on 2r vertices and C5[N2r] is the graph obtained from C5 by replacing each vertex with a graph isomorphic to N2r. 相似文献
996.
Tim Huber 《Journal of Mathematical Analysis and Applications》2009,350(1):135-146
In this paper we provide a new approach for the derivation of parameterizations for the Eisenstein series. We demonstrate that a variety of classical formulas may be derived in an elementary way, without knowledge of the inversion formulae for the corresponding Schwarzian triangle functions. In particular, we provide a new derivation for the parametric representations of the Eisenstein series in terms of the complete elliptic integral of the first kind. The proof given here is distinguished from existing elementary proofs in that we do not employ the Jacobi-Ramanujan inversion formula relating theta functions and hypergeometric series. Our alternative approach is based on a Lie symmetry group for the differential equations satisfied by certain Eisenstein series. We employ similar arguments to obtain parameterizations from Ramanujan's alternative signatures and those associated with the inversion formula for the modular J-function. Moreover, we show that these parameterizations represent the only possible signatures under a certain assumed form for the Lie group parameters. 相似文献
997.
We show that a complete equipartite graph with four partite sets has an edge-disjoint decomposition into cycles of length k if and only if k≥3, the partite set size is even, k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k. We also show that a complete equipartite graph with four even partite sets has an edge-disjoint decomposition into paths with k edges if and only if k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k+1. 相似文献
998.
Giovanni Mingari Scarpello 《Journal of Number Theory》2009,129(12):3094-3108
Text
A class of hyperelliptic integrals are expressed through hypergeometric functions, like those of Gauss, Lauricella and Appell, namely multiple power series. Whenever they can on their own be reduced to elliptic integrals through an algebraic transformation, we obtain a two-fold representation of the same mathematical object, and then several completely new π determinations through the above special functions and/or Euler integrals. All our π formulae have been successfully tested by means of convenient Mathematica®'s packages and enter in a wide historical/sound context of π-formulae quite far from being exhausted. Due to their structure, the formulae's practical value does not lie in computing π, but in allowing, through π, a benchmark for computing the involved special functions, particularly those less elementary.Video
For a video summary of this paper, please visit http://www.youtube.com/watch?v=UHZIHgAeCUc. 相似文献999.
The undirected power graph G(S) of a semigroup S is an undirected graph whose vertex set is S and two vertices a,b∈S are adjacent if and only if a≠b and a
m
=b or b
m
=a for some positive integer m. In this paper we characterize the class of semigroups S for which G(S) is connected or complete. As a consequence we prove that G(G) is connected for any finite group G and G(G) is complete if and only if G is a cyclic group of order 1 or p
m
. Particular attention is given to the multiplicative semigroup ℤ
n
and its subgroup U
n
, where G(U
n
) is a major component of G(ℤ
n
). It is proved that G(U
n
) is complete if and only if n=1,2,4,p or 2p, where p is a Fermat prime. In general, we compute the number of edges of G(G) for a finite group G and apply this result to determine the values of n for which G(U
n
) is planar. Finally we show that for any cyclic group of order greater than or equal to 3, G(G) is Hamiltonian and list some values of n for which G(U
n
) has no Hamiltonian cycle. 相似文献
1000.
Abdul-Majid Wazwaz 《Applied mathematics and computation》2009,211(2):495-501
Two (3 + 1)-dimensional shallow water wave equations are studied for complete integrability. The Hirota’s bilinear method is used to determine the multiple-soliton solutions for these equations. Moreover, multiple-singular soliton solutions will also be determined for each model. The analysis highlights the capability of the direct method in handling completely integrable equations. 相似文献